Fragmentation, Global Trade and Gravity�

Job Market Paper

Han (Ste¤an) QIy

Hong Kong University of Science and Technology

This draft: 20 November, 2013

Abstract

In this paper, I develop a Ricardian model of comparative advantage in tasks of production,

by modifying the Eaton and Kortum (2002) framework. I model fragmentation in a multiple-

country setting, taking into account trade costs. The model is able to explain the large gap

between bilateral gross trade and bilateral trade in value-added. Furthermore, I derive a gravity

equation that captures fragmented production and trade within multiple countries, which is

one of the �rst in the literature. Based on this result, I show that the bias caused by ignoring

fragmentation in the estimation of the gravity equation can lead to inaccurate estimation of

both trade elasticity and the competitiveness of countries in a systematic way. Moreover, my

model can explain the zeros in bilateral trade �ows.

JEL Classi�cation codes: F10, F11, F14, F17

Keyword: fragmentation, assembling center, double counting, gravity, bilateral, elasticity of

trade, competitiveness

�I am grateful to Edwin Lai, my thesis supervisor for guidance and encouragement. I am also grateful to the World

Bank for providing me with the disaggregate price data from the 2005 ICP round. I would like to thank Mario Crucini,

Kala Krishna, Jonathan Eaton, Andrés Rodríguez-Clare, Russell Hillberry, Larry Dongxiao Qiu, David Cook, Yao

Amber Li and Yong Wang for their helpful support and comments. Naturally, all errors are mine.yDepartment of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong

Kong. Email: ste¤an@ust.hk

0

1 Introduction

International fragmentation of production, which refers to the phenomenon that di¤erent tasks

of the process of producing a good are carried out in di¤erent countries, has become widespread

in recent decades. Likewise, the corresponding "triangular trade" between countries have become

more pervasive. The most well-known example of this production and trade pattern is the iPhone

and iPad designed by Apple. Apple purchased the sophisticated parts, such as touch screens,

cameras, processors, display and memories, from countries all over the world (many of them from

the North such as U.S., Germany, Japan, South Korea and Chinese Taipei) and shipped them to

Foxconn�s factories in Southern China. These parts would be further processed, assembled and

tested there, and became the �nal product, and then shipped to destinations all over the world

for consumption. Although China has become the "world�s factory" and the largest processing

exporter in the world, it is not the major player in international fragmentation. "Twin plants" in

Maquiladora emerged at the Mexico-US border after the establishment of NAFTA; processing trade

between the Central European countries and their EU neighbors surged after they joined the EU,

many ASEAN countries established export processing zones in 1990s. As a result, the domestic

value-added of a country�s exports can be much less than 100%. In May 2013, OECD and WTO

jointly released a dataset to account for trade in value-added (TiVA) among the major economies

in the world. If we compare the gross trade volume in the world and the total trade in value-added,

we will �nd that there is a large gap, and the gap is becoming larger over time. In year 1995, the

total trade in value-added in the world account for 94.4% of the gross trade volume in the world.

The ratio decreases to 84.8% in 2000, 80.2% in 2005 and 79.3% in 2008.1

In this paper, we develop a Ricardian model of comparative advantage in tasks, to better under-

stand international fragmentation, and the gap between gross trade and TiVA. While most of the

existing literature cares mostly about the trade in �nal goods, e.g. inter-industry and intra-industry

trade, we focus on the "intra-good" trade associated with international fragmentation. We develop

a model that describes the trade relationship between the source country of intermediate parts,

assembling centers and the destination for �nal consumption. The assembling center countries (e.g.

China in the iPhone example) import intermediate parts from foreign source countries (mostly the

more developed countries, the North) and assemble the �nal goods using the imported interme-

1For the gross trade volume of the world, we adopt the data from the PC-TAS (Trade Analysis system on Personal

Computer) from the International Trade Centre, based on exporters�reports of trade volumes, except for year 1995.

For year 1995, we directly adopt the data from NBER-United Nations Trade Data. If we use the importers�reports

of trade volume instead, which is usually higher, we will get 82.4% in year 2000, 77.8% in 2005 and 77.1% in 2008.

These ratios implies a even larger gap between TiVA and gross trade volume.

1

diate goods and domestic inputs. Then they re-export the �nal products to various destinations

all over the world. When the assembling center is also the consumption destination, there is just

trade in intermediate goods. When the assembling center is di¤erent from the �nal destination,

the value of the intermediate parts exported from the source country is counted as export from

the source country to the assembling center in the gross trade data, then counted again as part

of the value of the �nal good exported from the assembling center to the destination in the gross

trade data. However, this "double counting" problem in the gross trade data will not occur if trade

is documented in value-added terms. As more intermediate goods are traded in the form of this

"triangular trade", the gap between gross trade and TiVA becomes larger. Moreover, the TiVA

data include the value-added in service as part of intermediate inputs. These intangible services

associated with marketing and R & D, like the "headquarter services" in Helpman (1984), cannot

be directly re�ected in gross trade volume as they are by nature "nontraded". This issue has be-

come signi�cant as trade in services have become more and more important in recent years. But a

crucial question remain unanswered, how the assembling centers emerges? If the cost of producing

the goods in this "triangular" way is not lower than assembling them at the �nal destination, we

will have only trade in intermediate parts and no "double counting".

Our model suggests that the designer of the product (Apple in the iPhone example) will make

the decision of whether to o¤shore the assembling process based on cost saving. As a result,

lower input (labor) cost, higher technology capacity and shorter distance (lower trade cost) to the

destination country raises a country�s probability of becoming an assembling center. Labor cost at

the assembling centers needs to be su¢ ciently low to o¤set trade costs so as to justify o¤shoring.

If the labor cost of the assembling center is not signi�cant lower than the one in the destination

country, the extra trade costs of shipping the intermediate goods produced by the destination

country back-and-force will overcome the saving in assembling cost, which makes o¤shoring not

pro�table. Meanwhile, the extra trade costs of shipping other intermediate goods through the

assembling center should not be high. Thus the assembling centers usually tend to be closed to

the destination countries. The lower trade barriers between countries in the waves of globalization

also enhances o¤shoring. In this paper, the technology capacity of a country is interpreted as

its absolute advantage of production along the entire production process. For example, the larger

factory, industrial clusters, mature supply chain, better mobility and availability of labor contribute

to its higher technological capacity. By taking general equilibrium adjustments into consideration,

a country with large labor force tends to have its labor cost raising more slower thus serving as

the assembling centers for other countries. We test the theory and �nd that it can predict quite

accurately which countries are the main assembling centers.

Based on the model of fragmented production, we develop a gravity equation. The TiVA data

counts the exports of intermediate goods from the source country to the assembling centers directly

as the value-added from the source country to the destination country. Thus it avoids the "double

2

counting" problem in gross trade volume and serves as a better description of bilateral trade than

gross trade volume, based on our theoretical framework. Based on this theory, the bilateral gross

trade volume overstates the trade of the assembling centers and understates the export of the source

countries as well as import of the destination countries. The Northern countries usually play the

role of the sources of intermediate parts due to its high technology and the �nal destinations due

to its larger purchasing power. Meanwhile, the Southern countries with intermediate technology,

such as China, Mexico will serve as the assembling centers. As a result, the theory predicts that

using bilateral gross trade data, the elasticity of trade with respect to trade costs tends to be

over-estimated for Northern countries, and under-estimated for Southern countries. By comparing

the trade elasticities estimated using our gravity model, we verify this hypothesis. The systematic

di¤erences between Northern and Southern countries in the estimated coe¢ cients in a gravity model

has been attributed to asymmetric market penetration costs or asymmetric purchasing power in

the literature (See of Waugh (2010) and Fieler (2011)). However, we argue that the systematic

overstating and understating of trade volumes is a more important reason. Moreover, we �nd

that the competitiveness of the Southern assembling centers tend to be overestimated due to the

overstating of trade, while the competitiveness of the Northern countries tend to be underestimated

but in general not seriously a¤ected. This is consistent with our model prediction.

Basically, our paper bridges two groups of literature, the fragmentation literature and the global

value chain (GVC) literature. The �rst group of research has inspired our theoretical framework.

Baldwin (2006) has phrased the fragmentation phenomenon as the "second unbundling", which

refers to "the end of the need to perform most manufacturing stages near each other". In a

follow-up paper, Baldwin and Venables (2010) model two con�gurations of fragmentation, namely

"snake" and "spider". Our paper models international fragmentation in the "spider" manner:

countries specializing in di¤erent tasks export the parts directly to the assembling center. Some

papers model fragmentation in a "snake" way, i.e. countries progressively add value to a good until

it is �nished by the last country. An example is Costinot, Vogel and Wang (2013). Like our paper,

they also model fragmentation in a global general equilibrium, which can involve arbitrary number

of countries, and solve for a unique equilibrium. In equilibrium, countries with lower probabilities

of making mistakes at all stages specialize in later stages of production. We think that the "spider"

con�guration captures the relationship between supplier countries and "assembling center" better.

The production of the iPhone and iPad is a good example, as explained above. Other papers adopt

the "tradeable intermediate goods" setting to investigate international fragmentation, e.g. the later

part of Eaton and Kortum (2002) as well as the model in Alvarez and Lucas (2007). This approach

assumes that the aggregation of goods are used as either intermediate goods to produce other goods

or �nal consumption, and the expenditure share on intermediate goods is a constant. It is a short

cut to modeling fragmentation, but there is limitation to this approach. First, both the �nal goods

and the aggregation of intermediate goods are not tradable (though each of the intermediate goods

3

are tradeable). Thus there should be no gap between bilateral gross trade and bilateral trade in

value-added. This setting lacks the ability to account for the production chains associated with

the "triangular trade" we documented above. Second, the share of intermediate goods has to be

set as a constant and parameterized, which is an ad-hoc assumption. In fact, both the theoretical

predictions and results of the counter-factual thought experiment in the papers using this approach

crucially depend on the estimated value of this constant share. However, the estimated share of

intermediate goods in �nal production based on the global IO table is not constant over time. Meng,

Fang and Yamano (2012) use a global IO table and bilateral trade data to back out the value-added

contents in trade and reveal that the change over time of the share of intermediate goods in total

output is substantial in all countries/regions from year 1995 to year 2005. The large gap between

the estimated domestic value added (DVA) ratios of ordinary export and processing export in China

also strongly contradicts with this assumption. A possible solution to take care of these limitations

is to exogenously set multiple stages, as in Yi (2003) and Yi (2010). These two papers provide good

insights into the implications and signi�cance of the fragmentation of production. But the setting

of these papers are more applicable to North-North trade, as the US-Canada trade calibrated in

the model, rather than the "triangular trade" of the North-South-North type. The tractability of

the model can be greatly a¤ected when applied to multiple (more than 3) countries, even just for

calibration. In contrast, our paper can easily incorporate multiple countries and asymmetric trade

costs at the same time, which is among the �rst in literature as far as we know.

Besides the literature on fragmentation, the second strand of literature that is closely related

to our paper is the global value chain (GVC) literature, which focuses on the back-and-forth trade

between countries and the double-counting problem. Based on the pioneer work of Hummels, Ishii,

and Yi (2001), Koopman, Wang and Wei (hereinafter abbreviated as KWW) (2008), KWW (2012),

KWW (2013) and Johnson and Noguera (2012) have proposed various accounting frameworks, to

decompose the domestic and foreign contents in gross trade volume and link them to value-added

trade, with the help of input-output tables. Without these e¤orts on GVC, on which the TiVA

dataset is based, we could not carried out our empirical analysis. However, these accounting

methods need a theoretical foundation. Our paper can be viewed as a �rst attempt to �ll this gap

between the proposed accounting methods and its theoretical foundation. Thus our paper provides

a theory to explain the gap between the bilateral trade in value-added and bilateral gross trade.

The rest of the paper is organized as following. Section 2 introduces the basic multi-country

model and its implications on welfare, we also show how the assembling centers are determined.

Section 3 develops the gravity equation and test the gravity equation using world price and trade

volume data after the adjustments proposed by the theory in this section. Section 4 derives other

implications of the model. The last section concludes.

4

2 The Model

We begin by developing a model of Ricardian type with multiple countries along the line of Eaton

and Kortum (2002), (hereinafter abbreviated as EK) but extended to incorporate the fragmented

nature of the production of goods. Fragmented production is becoming much more common in

the past two decades, which brings new challenging for analysis of international trade, due to the

existence of large volumes of the "back-and-forth" trade between countries. Northern countries

supply the sophisticated intermediate goods to the poorer Southern countries, where the interme-

diate goods are assembled into the �nal product using domestic factor inputs. After that, a large

portion of the �nal goods are shipped back to Northern countries for consumption. In this model,

we will show how market forces shape international fragmentation and how production tasks are

allocated to di¤erent countries in the global supply chain.

Setting There are N countries in the world, indexed by n = 1; :::; N . Each country n has its

own labor endowment Ln, which serves as the only primary input in production for all tasks and

goods. The unit cost of labor is cn for country n. All the consumption goods form a continuum of

[0; I], with I increasing gradually through endogenous product innovation. Markets for intermediate

and �nal goods are perfectly competitive. Whenever an intermediate or �nal output is transported

from country n to country m, an iceberg trade cost �mn is incurred. That is, �mn > 1 units are

shipped from the source for one unit to arrive at the destination. As usual, we normalize �nn = 1

for all n and assume that the triangle inequality �mn�nl � �ml holds for 8l;m; n. In the rest of thepaper, all subscripts l;m and n refer to countries, and subscripts i and j refer to goods.2

Each country n possesses a technology stock of Tni in producing each good i 2 [0; I]. Like in EK,Tni re�ects country n�s absolute advantage in producing good i, which can be viewed as a summary

measure of the factor endowments for production other than labor, e.g. physical capital, human

capital, infrastructure and maturity of domestic supply network, etc. We also assume Tni = Tn in

the rest of the paper for simplicity. In other words, all the goods are symmetric; thus we can focus

on just one good.3 To analyze the fragmented production process, we index tasks of production

before assembling by a continuum of [0; 1], which is di¤erent from the original EK setting.4 After

these tasks are completed, the only task left is assembling.

Assumption All countries can undertake all tasks as well as assembling for all goods. Assem-

bling will take place only when the production tasks have been completed. The labor requirement for

2 In the rest of the paper, with no speci�c noti�ction, country l refers to the sourcing country producing intermediate

parts, country n refers to the assmebling center, country m refers to the destination of �nal consumption.3We can easily attend the setting by allowing countries to have di¤erent technology stock in di¤erent industries,

then each industry will act in the same way as the econmy in the basic setting.4The assumed measurement of 1 for all stages before assembling is just a standardization. It can be easily seen

later only the relative measurement of assembling process and all the processes before it, which is � matters.

5

assembling is equal to that of a measure � of tasks. The productivity in assembling is equal to the

productivity of producing all production tasks solely in that country.

In fact, it will make no di¤erence if we assume that the productivity of assembling is the same

for all countries. However, the above assumption simpli�es the analysis and describe the reality

better. For the simple good like furniture sold in IKEA, the time you spend to assemble it will

be usually much longer than those spent by their well-trained professionals. When a country has

a higher technology stock with regard to a good, the workers there know the good better. Thus

they tend to be also more e¢ cient in assembling the good. In practise we do not need to know the

exact value of �. Given the assembling center n, as we will show later, the tasks that each country

l undertakes in equilibrium will not be a¤ected by �. For a typical destination m, � will only a¤ect

the assembling allocation n. This means that we even can allow for di¤erent �i for di¤erent �nal

goods i, though we assume �i = � 8i here as we assume Tni = Tn. If assume �i to be di¤erent fordi¤erent i, a country may have more than one assembling centers, with di¤erent centers serving

di¤erent products. For example, it is possible that China possesses enough technology to assemble

the compact cars, but still import most of its luxury cars from other countries.

Consider a "spider" con�guration as described in Baldwin and Venables (2010). Suppose a good

is assembled at country n, and each country l will take charge of a measure knl of all the tasks

before assembling. In the rest of the paper, we shall use "stage" and "task" interchangeably. The

global production pattern will be as shown below. When l = m 6= n, the production pattern is

refer to as the "bilateral (back-and-forth) production" documented in Johnson & Noguera (2012),

which scaled down value added trade relative to gross trade; when l 6= m 6= n, this is refer to as the"multilateral (triangular) production" in that paper, which gives rise to indirect trade that occurs

via countries that process intermediate goods, and scale up the bilateral value-added trade.

6

Figure 1: Global Production Pattern

We follow Eaton, Kortum and Karmaz (2011) by assuming the measurement of stages produced

with productivity at least z is given by

knl

�1� exp

�� Tlknlz��

��;

which is parallel to the Fréchet distribution assumed in EK.5 Each country l possesses a �xed tech-

nology stock Tl for producing each good, and apply it to all stages of production. The productivity

draw for di¤erent stages might be di¤erent, but they come from the same distribution. When a

�rm in country l takes up those knl tasks, it draws the productivity for each stage from the same

distribution described above. However, when the country concentrates on fewer tasks, it has higher

probability of getting a higher productivity draw for each stage. This also re�ects the coordination

cost of undertaking di¤erent tasks within the �rm.

The cumulative labor requirement for country l producing k tasks is then equal to

fl (k) =R k0 zl (�)

�1 d�

As the stages form a continuum,R k0 zl (�)

�1 d� =R10 xdGl (x), where Gl (x) is the distribution of

zl (�)�1 and

Gl (x) = Pr

�zl (�) �

1

x

�= k

�1� exp

��Tlkx���

(1)

When k = knl, the cumulative labor requirement for country l will be

fl (knl) =R10 xdGl (x) = �

�1 +

1

�

�k1+ 1

�nl

T1�l

(2)

where � (�) is the Gamma function. Note that when knl = 1, the productivity of country l producing

all tasks on its own is equal to T1�l

�(1+ 1� ). When there is fragmented production, knl < 1. Thus the

per unit productivity will be 1fl(knl)

� T1�l

�(1+ 1� ), and per stage productivity will be T

1�l k

� 1�

nl

�(1+ 1� )� T

1�l

�(1+ 1� )

as well. Under our assumption, �rms tend to be more productive while they concentrate more in

the tasks they are good at. This gives rise to another bene�t of fragmentation besides cost saving.

As a result, fragmented production takes advantage of not only the di¤erence in labor costs across

countries, but also the comparative advantage of each country along the value chain. Countries

might be relative more productive for certain tasks compared with others. Fragmentation can allow

each country to focus on its core competitiveness, thus increasing global e¢ ciency.

5When knl = 1, which means that the whole process is produced solely in one single country, this expression will

degenerate to the original Fréchet Distribution.

7

With the derived unit labor requirements, regardless where the �nal consumption destination

is, as long as country n serves as the assembling center, the total cost of all tasks before assembling

is6

PNl=1 fl (knl) cl�nl = �

�1 +

1

�

�PNl=1

cl�nl

T1�l

k1+ 1

�nl

withPNl=1 knl = 1

Cost Minimization leads to knl =Tl(cl�nl)

��PN

m=1Tm(cm�nm)

�� . We denotePNm=1 Tm (cm�nm)

�� = �n for

simplicity in the rest of the paper. The corresponding total cost of all tasks (parts) before assembling

is

pn = �

�1 +

1

�

��� 1�

n (3)

in country n. The cost share of country l is cl�nl

T1�li

k1+ 1

�nl =�

� 1�

n = knl, which has similar functional

form to the expenditure share �nl in EK. However, the meaning of the expression is quite di¤erent

here. In EK, �nl represents the expenditure share of all �nal goods from country l in the total

expenditure of country n, where the goods from di¤erent countries are substitutable with each

other. An increase in the demand for goods from one country will reduce the demand for goods

from other countries. In our model, knl here represents the share of cost for all intermediate parts

from country l while the goods are assembled at country n. The intermediate goods from each

country are complementary to each other. When the assembling center n produces more goods,

the imports from all source countries will increase.

It is also noteworthy that the above equation applies as long as country n is the assembling

center, regardless of the value of �. The measure of assembling � will only determine where

the assembling location is, as we will see later. As long as the assembling location n is already

determined by cost minimization, the cost share of intermediate parts for each country knl will not

change with �. This property of the model is in fact important for us to derive the "adjusted"

gravity equation with costly assembling. As we shall present later, regardless of the number of

goods involved, as long as country n serves as the assembling center for destination m, the value

ratio of imported intermediated goods to domestic intermediate goods, knlkll will not be a¤ected.

2.1 Costless Assembling

Before we further investigate the total cost of producing at country n, note that the global trade

volume will appear quite familiar when � is negligible (= 0). In this special case, all goods will be

sold in the form of parts, like most furniture in IKEA. Regardless of the complexity of the good,

6The aggregation of intermediate parts here is in fact Leontief type. However, if we change the aggregatin to CES

type, all the �llowing result will not be qualitatively di¤errnt.

8

consumers can easily assemble it by their own hands and accept the goods in this form. Under

this setting, all assembling will take place at where consumption is. This simply follows

�ml � �mn�nl as

�� 1�

n �mn =hPN

l=1 Tl (cl�nl�mn)��i� 1

�

�hPN

l=1 Tl (cl�ml)��i� 1

�= �

� 1�

m

When producers can assemble goods with no cost, the production (assembling) will be located

where demand is so as to save extra trade costs. In this case, pn also re�ects the actual price of

each good in country n, as in EK. knl captures both the measure of stages carried by country l,

and the cost share of country l. Thus the expenditure share of (intermediate) goods imported from

country l isXnlXn

= knl =Tl (cl�nl)

��

�n(4)

) Xnl =

��nlpn

���XnPN

m=1

��mlpm

���Xm

Yl

=XnYl (�nl)

��

�n�l(5)

where Xnl is the trade volume from country l to country n, Xn is the total consumption of country

n, Yl =PNm=1Xml is the total sales of country l and �l =

PNm=1

(�ml)��Xm�m

re�ects the multilateral

resistance of the exporting country.7 This is in fact a gravity equation. In fact, the Anderson

(1979) model, Eaton and Kortum (2002) model and Melitz (2003) type model in Chaney (2008)

all leads to the same structure of gravity equation shown above. The main di¤erence here is the

all imports from other countries are intermediate parts, rather than �nal goods, as each country

will take charge of the assembling of all �nal products for domestic consumption. As m = n always

holds, there is no trade in �nal goods. Thus neither "bilateral (back-and-forth) production" nor

"multilateral (triangular) production" as described in Johnson & Noguera (2012) exist. As a result,

we will have no goods with the production process like an iPhone in the economy.

Besides this, the economy also exhibits the following properties

Lemma 1 When assembling cost is negligible, the measure of tasks carried out by each country is

equal to the expenditure share of that country�s export in the destination country. Welfare gains

from trade is only related to domestic expenditure share and the e¢ ciency dispersion parameter �.

7This equation direct follows equation (11) of Eaton and Kortum (2002). Reader can also refer to Anderson and

van Wincoop (2003) for detailed derivation.

9

Real wage in country n in term of good i is

cnpn=

1

��1 + 1

�

� � Tnknn

� 1�

Compared with autarky, where knn = 1 and each country produce all parts domestically, welfare

is augmented by k� 1�

nn . This feature of gains from trade is documented by Arkolakis, Costinot,

and Rodríguez-Clare (2012). It is interesting that it continues to here for fragmented production.

However, this free assembling assumption is unrealistic, the result will be di¤erent when � > 0.

In equilibrium, the wage {cl} in each country is determined by labor market clearing condi-

tions. In any country l, the total labor demanded to produce intermediate parts for �nal consump-

tion of any possible destination (including l itself) should be equal to the total labor endowed in

country l, Ll. We can use the following expressions to describe this relationship.

XN

m=1�ml

24��1 + 1�

�k1+ 1

�ml

T1�l

� cmLmpm

35 = Ll, 8l (6)

The above equations form a system of N equations and N unknowns. However, as the last equation

in the system will be automatically satis�ed as long as the other N �1 equations hold, the solutionwe obtain from the above system in fact describes the relative wage in any pair of countries. This

system also has a unique solution, and we leave the proof to the appendix.

Proposition 1 In a costless assembling world, the labor market clearing in each country gives a

unique set of {cl} in equilibrium once one country is chosen to be numeraire.

To understand the equilibrium in a more intuitive way, we look at a special case with symmetric

trade cost (�nl = � , 8l; n)8, in which the model can be explicitly solved. Under the symmetric tradecosts,

kml =Tl (cl)

��PNi=1 Ti (ci)

�� ; kmm =Tm (cm)

��PNi=1 Ti (ci)

��

Under this speci�cation, kml is the same regardless of the destination m, each country will perform

the same measure of tasks for any good consumed in the world. Furthermore, any goods consumed

will require ���1 + 1

�

� k1+1�

ml

T1�l

unit of country l labor. Thus for any country l,

k1+1

�ml

T1�l

Ll=Tl (cl)

�(�+1)

Ll�hPN

i=1 Ti (ci)��i�(1+ 1

� )

8Here we need to assume � ll = � , 8l as well. To be consistent with the previous setting � ll = 1, we might need torestrict �nl = 1, 8l; n. Thus there is free trade everywhere.

10

is a constant, which leads to9

LlT1�l

LnT1�n

=

�kmlkmn

�1+ 1�

(7)

) clcn

=

�Tl=LlTn=Ln

� 11+�

: (8)

The corresponding measure of tasks each country l takes care of will be

kml =L

��+1

l T1

�+1

lPNi=1 L

��+1

i T1

�+1

i

If we use Di = LiT1�i to denote country i�s competitiveness, then kml =

D1

�+1lPN

i=1D

1�+1i

for any possible

destination m. In this free assembling world with symmetric trade costs, the country with higher

competitiveness will take charge of more tasks in the production process, thus becoming more im-

portant in the world economy. Assuming no population growth sand no migration across countries,

the shift in a country�s competitiveness comes from the growth in technology stock. The surge in Tl

will not only make country l more important in the world�s economy, but also bene�t the workers

in country l through the increase in real wage.

When we control for the trade costs across countries, the equilibrium wage in each country is

only related to the technology stock and labor endowment of that country. For a country with

higher technology stock, the wage will also be higher due to this absolute advantage in technol-

ogy. Although higher wage will give the country disadvantage in production, the positive e¤ect of

technology outweighs the disadvantages and enables the country to undertake more tasks along the

value chain. At the same time, larger population will induce more competition among the workers,

thus bring down the wage. Lower wage will make the country more competitive in the international

market, and take charge of more tasks for any given destination. For any destination m, real wage

cmpm

=1

��1 + 1

�

� � Tmkmm

� 1�

=1

��1 + 1

�

� �TmLm

� 1�+1

�PNi=1 L

��+1

i T1

�+1

i

� 1�

will increase with Tm and decrease with Lm.

2.2 Costly Assembling

The special case of � = 0 serves as a benchmark. We now investigate the case with positive �

and see the di¤erence. As the productivity at assembling stage is the same as autarky production,

���1 + 1

�

�T� 1�

n units of workers is required to �nish the production, if the assembling takes place

9 It is easy to verify that above solution satis�es equation (6).

11

in country n. The total cost of the �nal good is

Pn = �

�1 +

1

�

���� 1�

n + �cnT� 1�

n

�= �

�1 +

1

�

��� 1�

n (1 + �k� 1�

nn )

At destination m, the price of the good will be Pn�mn = ��1 + 1

�

��mn�

� 1�

n (1 + �k� 1�

nn ). Real wage

becomescm

Pn�mn=

1

��1 + 1

�

� T1�m

�mn�nmk1�nm(1 + �k

� 1�

nn ):

When n = m, which means the assembling has not been o¤shored, real wage becomes

cnPn

=1

��1 + 1

�

� T1�n

k1�nn + �

Compared with autarky (knn = 1), welfare is augmented by (1 + �) =�k1�nn + �

�. Note that

1 + �

k1�nn + �

<1

k1�nn

as long as knn < 1. The gains from trade is now not only related to domestic expenditure share and

the e¢ ciency dispersion parameter �, but also to the measure of assembling �. Therefore, the gains

from trade is smaller than what is proposed in Arkolakis, Costinot, and Rodríguez-Clare (2012)

when fragmentation is taken into consideration. To sum up

Lemma 2 When assembling cost is not negligible, Welfare gains from trade is smaller than k� 1�

nn

proposed by Arkolakis, Costinot, and Rodríguez-Clare (2012).

Interestingly, this result coincides with Arkolakis, Costinot, Donaldson and Rodríguez-Clare

(2013), although the reason for the smaller gains from trade is di¤erent.

However, as each destination m will search for the cheapest source for assembling, it will take

place at country n i¤

Pn�mn = minlPl�ml

which is equivalent to �mn�nmk1�nm(1 + �k

� 1�

nn ) � �ml� lmk1�lm(1 + �k

� 1�

ll ) for all l = 1; :::; N .

Similarly, o¤shoring of assembling is pro�table for countrym if Pm > Pn�mn, which is equivalent

to k1�mm(1 + �k

� 1�

mm) > �mn�nmk1�nm(1 + �k

� 1�

nn ). Taking the changing of tasks performed by each

country out of consideration (kmm � knm), the cost saving in assembling must compensate for theextra trade cost of shipping the domestically produced intermediate parts twice (back and forth,

which is captured by the term �nm�mn).

12

Although in general it is hard to determine the assembling location as there involves too many

parameters, some general statement can be made.

Proposition 2 Shorter distance to the destination country, lower labor cost or higher technology

stock will increase the probability of a country being the assembling center for the destination

country. A country can also implement the policy of lowering trade barrier for intermediate inputs

to increase its chance to become a assembling center.

Smaller geographic distance in general leads to both lower �nm and �mn for the country n and

destinationm. Lower cn or higher Tn re�ect that country n has a stronger comparative advantage in

producing the good, which increases knn and decreases knm. The country will carry out more tasks

along the supply chain compared with other countries. Lowering trade barriers �nl for intermediate

goods increases �n, which leads knm to decrease as well. All these actions enhance the country�s

competitiveness in the supply chain and reduce Pn�mn. (As k1�nm(1 + �k

� 1�

nn ) is lower). Thus its

chance to become the assembling center for country m increases.

[Table 1 Here]

By comparing the bilateral TiVA data with bilateral gross export data, we can in fact identify

the assembling centers. Table 1 reports the gross export and TiVA export of major developed and

developing countries in the year 2005. From the table, it is clear that both the volume and share

trade of each country vary a lot while considering TiVA instead of gross trade. While the gross trade

volume and gross trade shares understates the importance of most developed countries (except for

the economies with a major port), they overstate the importance of the trade of many developing

countries at the same time. Moreover, we can observe that China�s exports are very di¤erent from

those of other BRICS countries, and they behave more similarly to ASEAN countries. Its large

trade volume, which is comparable to the largest developed countries, makes it special. Other

BRICS countries do not have many back-and-forth trade and they export a lot of raw materials.

Moreover, the exports of other assembling center countries are far less diversi�ed than China. For

example, 85% of Mexico�s exports go to United States. For all the ASEAN countries listed in the

table, United States, Japan, Singapore and China are the four largest exporting destinations, and

exports to these countries account for more than 50% of the total exports for each of them.

In year 2005, global trade volume is 25% larger than global trade in velue-added. We use this

as the threshold to determine the assembling centers. For each pair of countries, we divide the

bilateral gross export by the bilateral trade in value-added (TiVA) to get a ratio Anl. We then

de�ne the exporting country as an assembling center for the destination country if the ratio is

large than 1:25, as it contributes to the gap between gross trade and TiVA more than the world

13

average.10 Interestingly, except for the countries with a major port,11 the countries serve more as

assembling centers in our sample are China, ASEAN countries and Central European countries,

the usual assembling centers in our mind. All these assembling centers under our de�nition seem

to satisfy the proximity-to-destination, lower-labor-cost and high-technology-stock characteristics.

Mexico is right next to its major exporting destination, North America and enjoys much lower

labor cost. Its technology level is also signi�cantly higher than the nearby Caribbean countries.

As a result, a standard trade and production pattern in this region will be: intermediate parts are

made in the United States, then exported to Mexico where the parts are assembled into goods;

these goods are exported back to the United States or Canada for consumption. Similar pattern

can be observed between Central European countries like Czech Republic, Hungary, Poland and

their Western European neighbors like Germany and France, or between the ASEAN countries and

Japan or even ASEAN and China. Another contributing factor to assembling center status is lower

trade costs for intermediate goods. This refers to for example the Free Trade Zones (processing

zones) seen in many developing countries. Countries give tari¤ rebates to the imported inputs and

sometimes preferential tax treatment to the �rms in the zone.

Next, we directly test Proposition 2. As in EK, for each pair of countries, we use b�nl = max 2i

pn(i)pl(i)

to proxy for bilateral trade cost �nl, where pn (i) are from the ICP 2005 round and max 2 denotes

the second highest value. We also use relative GDP per capita to proxy for the relative wage,12

and the relative amount of patents �led and average years of schooling of citizens to stand for

technology level. We then run the following Logit regression and OLS regression

lnAnl = �0 + �� lnb�nl + �C ln clcn + �P ln RlRn + �H ln HlHn + "nlwhere cl is proxied by GDP per capita, Rl is proxied by total number of patent �led and Hl is

proxied by the average years of schooling of country l. We obtain the result as listed in Table 2.

[Table 2 Here]

It is clear that all the coe¢ cients are signi�cant and of the correct sign. When we drop the

5 countries with major ports as exporters, the result become even more signi�cant. A large Anl

indicates that a larger portion of the country l�s export to country n are in fact value-added from

other countries, thus country l serves more as an assembling center for country n. As a result, our

Proposition 2 is strongly supported by empirical evidence.

10We also use other thresholds as 50%, 100% for rebustness check.11They are Hong Kong, Singapore, Belgium (Antwerp), Netherland (Rotterdam) and Germany (Hamburg).12We use it as the actual average wage data for all the sampling countries is hard to obtain, and empirically average

wage is strongly correlated to GDP per capita.

14

Next, we investigate the domestic value added (DVA) ratio in the exports of an assembling

center n. The DVA ratio is given by

knnpnPn

=knn

1 + �k� 1�

nn

which is increasing in knn =Tn(cn)

��

�n, the measure of intermediate tasks carried out domestically.

When Tn increases, or cn decreases, country n tends to have a stronger comparative advantage in

producing the good. It will undertake more intermediate tasks and import fewer intermediate parts

from other countries. As a result, the DVA ratio also rises.

Corollary 1 Lower labor cost, higher technology stock, or lower trade barriers for interme-

diate inputs will enable the assembling center country to produce more intermediate parts (tasks)

domestically, and thus to attain a higher domestic value added ratio in its exports.

This prediction is consistent with the empirical �ndings in Kee and Tang (2013). During the

period 2000-2006, there was a signi�cant increasing of the DVA ratio for China�s processing export.

At the same period, there is also evidence that the absorption of technology in China is faster than

other countries in the world, e.g. the large increase in foreign patents applied in China (1441 in year

1997 to 28007 in 2005, while the increasing rate for other major economy in the world is less than

50%). Although the patents are foreign-owned, and the production technology might be within

the multinational entrepreneurs, certain stage of production would still be carried out in China,

and the technology di¤usion both within and between �rms would be signi�cant. With this big

increase in TChina and relatively stable labor cost (the large population of China plays a role here),

the processing-trade �rms in China tend to use more domestically produced parts, rather than

imported ones, and this contributes to an increasing DVA ratio. In Kee and Tang (2013), they also

�nd signi�cant drop in both the number of variety and volume of imports of foreign intermediate

parts during that period, which are consistent with the prediction of our model above.

Apart from the above partial equilibrium e¤ects, there is also general equilibrium adjustment

in this world with costly assembling. The set of labor cost fclg of each country, the set of technologystock fTlg and the set of trade costs f�nlg determine the global production pattern. For eachcountry m, there is an unique assembling center n, which spends extra labor to assemble the

product. 13 Following this, we have the labor clearing conditions

XN

m=1

24�mn��1 + 1�

�k1+ 1

�mn

T1�n

� cmLmPm

35+Xm2n

�mn���1 + 1

�

�T

1�n

cmLm�mnPn

= Ln, 8n (9)

where m is the set of countries who uses country n as the assembling center. The LHS of the above

equation consists of two parts. The demand of labor may come from the production of intermediate13The conclusion of uniqueness of assembling center can be easily loosen if we allow for hetergeneity in technology

stock Tni or measure of assembling �i for di¤erent goods i.

15

tasks for either domestic or foreign consumers, but it may also come from the assembling process

when the country is an assembling center for itself or other countries. Now we have n equations of

labor market clearing and n unknowns fclg, which will determine the equilibrium. Note that thesecond part of the LHS of equation (9) decreases with cn but increases with ci (i 6= n). Thus wehave

Proposition 3 The set of labor cost fclg is endogenously and uniquely determined in equilibriumonce one country is chosen to be numeraire.

� A Two-Country Example

Although the equilibrium is still uniquely determined by the labor market clearing conditions,

how exactly the equilibrium works will still be complex. Here we will present a simply example

of 2 countries with symmetric trade cost to illustrate the major di¤erence between the costless

assembling (� = 0) and costly assembling (� > 0) cases. We denote the two countries by A and B,

with technology stock TA and TB, and labor endowment LA and LB respectively. We also assume

that �AB = �BA = � to simplify the analysis.14

In this two-country world with symmetric trade cost, it is straightforward to obtain the measure

of intermediate tasks performed by each country in assembling center A, under both costless and

costly assembling

kAA =TAcA

��

TAcA�� + TB (�cB)��; kAB =

TB (�cB)��

TAcA�� + TB (�cB)��= 1� kAA;

kBB =TBcB

��

TA (�cA)�� + TBcB��; kBA =

TA (�cA)��

TA (�cA)�� + TBcB��= 1� kBB:

Then in each assembling center i (= A;B), to produce one unit of good, � iA��1 + 1

�

� k1+1�

iA

T1�A

unit of

country A labor and � iB��1 + 1

�

� k1+1�

iB

T1�B

unit of country B labor is required.

1. When � = 0

LAkAA + �LBT

1�B

T1�A

k1+ 1

�BA

k1�BB

= LA

As shown in the appendix, cAcB

will decrease with LALB

in this case. Equilibrium is easily

determined by relative labor endowment and above equation.

2. When � > 014 If we further assume that �AA = �BB = � instead of 1, the analysis will be even further simpli�ed.

16

It is possible that each country assembles its own �nal consumption, or a country assembles

all the goods. When cA is very large, country B will assemble all the goods. Within this

range, the labor market clearing (LMC) condition gives a downward sloping relationship

between cAcBand LA

LB. Then if the competitiveness of the country A increases, then kAA will go

up, until country B assembles all the goods can not be a equilibrium. In this case, country

A�s consumer will be indi¤erence between the two possible assembling centers. When A�s

competitiveness increase further, each country will assemble for its own �nal consumption.

To the opposite, if cB is very large, country A will assemble all the goods. Thus we can draw

the following �gure to describe the the relationship between LA=LB and cA=cB under this

2-country setting. All the derivation is presented in the Appendix. We can also show that

similar pattern holds for the relationship of relative technology level TA=TB and cA=cB.

Figure 2 : The Determination of Relative Wage in 2-Country Economy

3 Gravity Equation and Application

3.1 Bilateral Trade Volume

An important feature for the "triangular trade" we document is that its existence calls into question

running gravity equation using data for gross trade �ows. With zero assembling cost, the gravity

equation (5) is applicable to bilateral trade volumes. However all the �nal goods will be like the

IKEA furniture. Consumers purchase the whole set of parts from the retailers and assemble them

into �nal product by themselves with no extra cost.

17

When assembling is costly, equation (5) is no longer valid. However, for a assembling center n,

regardless of whether the consumption destination of the good is domestic market n or some other

country m, we will still have

knl =Tl (cl�nl)

��

�n, kll =

Tl (cl)��

�l

) knlkll

=�l�n

� ���nl (10)

where knl re�ects the both the measure of tasks and cost share of intermediate parts from country l

to country n, and kll re�ect both the measure of tasks and the cost share of domestic intermediate

parts. When � = 0, knl =XnlXn

and kll =XllXl, equation (10) is exactly the equation (12) in EK. And

we will rerun this equation log�XmlXm

=XllXl

�= Sl�Sm� ��ml using more recent data to serve as the

benchmark.

For a destination country m, the �nal consumption can either be assembled domestically or at

the unique assembling center of it, country n.15 We rede�ne the total consumption of country m,

Xm = Vm + Am, where Vm represents the value of all the intermediate parts and Am represents

the assembling costs (either in country m or from the assembling center country n). As there

might be various di¤erent assembling locations, Vm = Vmm + Vmn�mn, where Vmm re�ects the

value of the intermediate parts assembled in country m which goes to country m�s consumption,

and Vmn re�ects the value of the intermediate parts assembled in country n which goes to country

m�s consumption. If all the goods are domestically assembled at country m, Xml = Vmmkml. When

all the goods consumed at country m are assembled at country n, Xnl = Vmnknl will be counted as

country l�s export to country n instead. Thus

knl =XnlVm

, where m is the �nal destination,

which can be either m or n. The reality will usually between these two cases. When m = n, the

situation is simple, we just use Vn to replace Xn in equation (4). When m 6= n, intermediates

imports from a third country l to assembling location n should be counted in country m�s import

Xml in the gravity equation when gravity equation holds with � = 0. However, it turns out to be

counted into country n�s import Xnl and counted again in country n�s export to country m, Xmn.

15This is due to our assumption of Tni = Tn. If we add back the heterogeneity across goods, the uniqueness keeps

to hold for each good i. If we instead allow for di¤erent measurement of assembling process, � for di¤erent goods,

we can have di¤erent assmebling locations for goods consumed at country m.

18

After we adjust it to be country l�s export to country m as shown below16, we will have

X 0ml=VmX 0ll=Vl

=kmlkll

=�l�m

� ���ml

) X 0ml=XmX 0ll=Xl

=�l=vl�m=vm

� ���ml (11)

where vl = VmXm

and X 0s refer to the bilateral trade volume after the adjustments of counting the

trade volume of the intermediate goods from country l to assembling center n back to Xml, the

trade volume from country l to destination country m. Note that this adjustment is in fact based

on the counter-factual case in which goods are assembled and at destination m.

Taking log of the above equation, we have

log

�X 0ml

Xm

�� log

�X 0ll

Xl

�= Sl � Sm � ��ml (12)

Although the equation becomes somehow di¤erent from the equation (12) in EK, Sl = log (�l=vl)

and Sm = log(�m=vm) still can be treated as country �xed e¤ect while estimating it.

Figure 3: Accounting of Bilateral Trade Volumes

If o¤shoring of assembling takes place, the trade volume of the assembling country is greatly

magni�ed by the "back-and-forth" trade, while the intermediate good exporter�s trade volume to

the �nal destination is reduced.17 This predicts that, the gravity equation estimation based on

more recent years data will reveals smaller estimation of �, as more "double counting" happens

with this fragmented production. The estimation will be smaller for Southern countries, and

larger for Northern countries. In reality, the evidence for Northern countries might be more clear

16 Ideally, we should also count for the di¤erence in kml and knl while the assembling location has changed. But

this is the second-order compared to the miscounting of the trade volume of intermediate goods to the assembling

center. To actually adjust for it, we need the infromation about the share of intermediate goods from each supplier l

while the good is produced at destination m instead of assembling center n. This is really hard to obtain in practise.17For the destination country�s import from the intermediate exporter, it is missed as well.

19

compared with Southern countries. As the technology stock of the Southern countries, such as

China, Mexico and the Southeast Asian countries increase, the chance of those countries to serve

as the assembling center for other country will become higher. Thus more overstating of both the

import and export volume of these assembling centers will take place for trade with these countries

compared with the � = 0 benchmark.18 As a result, the estimated � will be lower than its real

value for Southern countries. Similarly, the rich countries� intermediate export of parts are not

counted into the bilateral trade volume toward its destination, most probably another rich country.

Thus the estimated � will be larger than its real value for Northern countries. Thus we have the

following proposition

Proposition 4 In a world with back-and-forth trade, the estimated e¢ ciency dispersion parameter

� trends to be lower for the assembling o¤shoring centers, and higher for the intermediate parts

exporter and consumption destinations.

In other words, in order to �x these biases caused by fragmentation in bilateral trade �ow data,

one might have to reallocate the intermediate imports of the assembling centers for re-export to be

the export to the destination country from the intermediate input exporter. The role of countries

in the global supply chain is not naturally exclusive, a country can be the assembling center and

intermediate part producer at the same time. However, due to Proposition 2, the assembling center

is usually a Southern country with relatively high technology stock, e.g. China. At the same time,

Northern countries are capable to take charge of intermediate parts and consume more, due to

their higher technology stock and larger economy size. As a result, the back-and-forth trade we

describe above usually takes the North-South-North form. Thus the North-North bilateral trade

volume in equation (11) will be understated, while the North-South and South-North trade volume

will be overstated. For the same true value of �, directly estimating equation (11) will leads to a

higher estimation of � for North-North trade, but possible lower estimation for North-South and

South-North trade. The e¤ect on South-South trade is not clear. These are consistent with the

�nding in Waugh (2010).

All Countries OECD Countries Non-OECD Countries

Estimation of � 5.5 7.9 5.5

Estimation of Trade Elasticity in Waugh (2010)

As the result shows, The within OECD estimation is much higher than overall estimation

of �. Although the result for North-South and South-North trade is not reported, it must be

lower than 5.5 as the estimation for the other two subgroups are no lower than 5.5. He uses

18However, the e¤ect will be less clear for South countries. When the technology stock increases, a country will

also supply more intermediate parts for other countries at the same time.

20

asymmetric trade cost to explain the phenomenon and it serves as the major contribution of his

paper to the literature. Our model gives another possible explanation for this empirical �nding,

beside Waugh�s approach. However, when the competitiveness of the country increases with the

consistent technology upgrading, the tasks performed by these countries also increases. In the end.

it serves as only intermediate goods supplier but not assembling center for a destination country,

its trade with the destination will also be understated.

3.2 Empirical Estimation

To adjust for the double counting problems caused by fragmentation in bilateral trade �ow data,

we need to account for the back-and-forth trade in all assembling centers and restore the value of

exports from the intermediate good supplier to the �nal destination. The portion of its exports

to the destination countries which comes from imports of intermediate goods should be subtracted

from both its exports and imports and counted as export from the intermediate good supplier to

the �nal destination country. However, this is hard in practise. First, it requires detailed trade

data for all the assembling centers. Second, it is hard to distinguish imports of �nal goods and

intermediate goods for most countries. Furthermore, the Northern countries may also take charge of

the assembling, or �nal production job for nearby countries if its competitiveness is strong enough.

Although the adjustment is hard in principle, the recent Trade in Value Added (TiVA) data, the

product of an OECD-WTO joint project, published in May 2013 has accounted for exactly what

we desire. This project makes use of the global Iuput-Output table and the recent development

of methodology in the Global Value Chain (GVC) literature, and gives estimation of the trade

volumes in value-added between each pair of countries. This recently available dataset makes it

possible to more accurately estimate the gravity equation taking fragmentation into consideration.

In the following, we shall estimate the gravity equation estimation based on both the traditional

method and the method proposed in this paper. Then we can see the bias caused in the gravity

equation estimation when we ignore the fragmentation nature of the production. Not only is the

trade elasticity �, but also the country �xed e¤ect, signi�cantly a¤ected. As the country �xed

e¤ect stands for the competitiveness of a country, these bias will lead to stronger bias while these

measures of competitiveness are used for further analysis or estimations.

To carry out a fair comparison, we include the 56 economies covered by the TiVA data in our

sample, and take the 1990 OECD countries used in Eaton&Kortum (2002) as the group of Northern

countries.19 Our sample countries consist of more than 95% of global production and more than

92% of global trade volume is captured by our sample economies.

19The OECD group has expanded from 19 countries to 34 countries from 1990. However, the original members

stands for a better sample of the industilized and developed countries. In the 15 new members who joins after 1990,

many of them clearly serves as an assmebling center for neighbor countries, e.g. Mexico and those Central European

countries.

21

Next, we describe those data and how the data are used in this paper in detail. For estimation

based on gross trade volume, we follow EK in the following manner:

XnlXn

=Importsnl

Gross Mfg. Productn � Total Exportsn + Total Importsn(13)

XnnXn

= 1�X

l 6=nXnlXn

(14)

and use b�nl = max 2i

pn(i)pl(i)

to simulate �nl. EK also use

Dnl =lnb�nl

meani

hln pn(i)pl(i)

ito measure what the price index in destination n would be for a buyer there who insisted on

purchasing everything from source l, relative to the actual price index in n (the price index for a

buyer purchasing each good from the cheapest source). The Mean of ln pn(i)pl(i)in the denominator is

for the 60 tradable sectors, and stands for the di¤erence in aggregate price index of tradable goods

in county n and l.20 We replicate Table II in their paper using the more recent the disaggregated

price level data from ICP 2005 and obtain the results listed in Table 3.

[Table 3 Here]

Note that for this group of OECD countries in 1990, we take the minimum and maximum

within the group, to make it comparable with the Table II in Eaton & Kortum (2002). When we

make the comparision, it is clear that the range of Dnl within the OECD group did not change

much from 1990 to 2005, which means that the geography or distance still matters after the period

of 15 years as there might not been signi�cant improvement of transportation technology in this

period. However, we can observe that the Maximum source and destination has been concentrate

much more to the few countries, U.S., Canada and Japan. This re�ects the fact that the European

developed economies have been integrated more after the establishment of EU. In this manner, the

geography matter even more in recent years. Similar as Table 3, we construct the same table for

the rest of the countries in our sample, the newly joined OECD countries after 1990 and the major

developing economies outside OECD. We construct the same measure and take the minimum and

maximum among the whole sample. The table 3a and 3b in the appendix report the results for

the new set of OECD countries and non-OECD countries separately. It is noteworthy that the

ranges of Dnl for the other countries are not much di¤erent from the numbers in Table 3 for OECD

countries. This further supports our view that geography still matters much.

We have already seen the estimation results of Waugh (2010), which is based on the bilateral

trade volume and ICP data at year 1985. He did not take fragmentation into consideration, and

20meani

hln pn(i)

pl(i)

i= mean

iln pn (i) �mean

ipl (i) is exactly the di¤ernce in the log of the aggregate price index of

the tradable goods in these two countries.

22

this omitting tends to be more severe in recent years, as shown in the di¤erence between gross trade

and TiVA. The di¢ culty for Southern countries to export, which is captured by the �xed exporting

e¤ect in Waugh (2010) should not be the only reason for the systematic asymmetry between North

and South, at least not anymore in recent years. To show it, I follow Waugh (2010)�s method,

but using more recent data for year 2005 instead. We adopt the importer�s report to be consistent

with the domestic production data from the International Yearbooks of Industrial Statistics. To

estimate for trade costs across countries, we obtain the PPPs and Expenditure Data at the Basic

Heading level for all countries for ICP 2005, and use

b�nl = max 2i

pn (i)

pl (i)

to simulate �nl as Waugh (2010) and EK. After obtain the necessary data, we run the OLS regression

following equation (10), with Sl and Sm expressed by the log of aggregate price indexes in Dni.

We also run the regression for the pooled data, OECD subgroup, non-OECD subgroup and cross

OECD and non-OECD subgroup respectively. The results are in Table 4

All Countries OECD Countries Non-OECD Countries Other Pairs

Estimation of � (year 2005) 6.10 (0.07) 6.31 (0.18) 6.50 (0.12) 5.77 (0.09)

Table 4 : Estimation of � using the ICP 2005 data

It is clear that the estimation for OECD group is still larger than the pooled sample, and the

estimation for North-South and South-North trade is smaller than the pooled sample, although the

di¤erence is smaller than the ones in Waugh (2010) for the estimations of year 1985. This reveals

that the systematic asymmetry between Northern and Southern countries still exists after 20 years

of time. To get sharper result, we can focus on the trade between the Southern assembling centers

and their OECD partners. Here we make the simplifying assumption that for a pair of assembling

center country and its OECD partner, the trade �ow from the assembling center to the OECD

partner is �ow of �nal goods, while the trade �ow from the OECD partner to the assembling center

is �ow of intermediate goods for the same set of �nal goods. Thus, we assume that there is a typical

processing trade pattern. According to our theory, bilateral gross trade �ows overstate bilateral

trade in value-added. We match each assembling center with the corresponding �nal destination

according to our de�nition in Section 2.2 (Anl > 1; 25). The �nal destination is treated as the

OECD partner. The trade �ow from the assembling center to the OECD partner is treated as �ow

of �nal goods. The trade �ow from the OECD partner to the assembling center is treated as �ow of

intermediate goods for that same set of products. We then run the same regression as above based

on this selected sample of Southern and Northern countries. We get an estimated elasticity of trade

of 5:31, with a standard error of 0:15.21 The elasticity of trade between assembling centers and

21Here we restrict the assembling center to be a non-OECD country, and the destination to be a OECD country.

23

their partners is signi�cant smaller than the one for All Countries (6.10), and the one for OECD

countries group (6.31). This implies that, controlling for trade costs, the OECD countries trade less

with each other in gross terms compared with the world average. But the assembling centers trade

much more with their partners compared with the world average, controlling for trade costs. Later

we will run the same gravity regressions based on the adjusted data, so as to make comparisons.

We then follow the method proposed by EK, to sort the distance between pairs of countries into

6 categories, [0,375), [375,750), [750,1500), [1500,3000), [3000,6000) and [6000,maximum) miles.22

We also control for whether the two countries has a shared border, shared language, or a regional

free trade agreement (RTA) between them. The results are shown in Table 5. Similar to what EK

(2002) obtained, the coe¢ cient on distance decreases as the distance between the pair of countries

increases. Shared border or shared language has a positive e¤ect on trade volume, while the e¤ect

of the regional free trade agreements do not have a signi�cant role here. A possible explanation for

the insigni�cant e¤ect of the RTA is that, the tari¤ and other non-geographic barrier between the

OECD countries is already low, thus the e¤ect of free trade may not be as strong as people may

think.

[Table 5 Here]

In Table 5, the variable Si is a measure of competitiveness. As in EK, we normalize by settingPi Si = 0. As shown in Table 5, compared with the results in EK, the magnitude of the Si becomes

smaller in general, which indicates that the di¤erences in the competitiveness within the OECD

countries become smaller. The convergence in technology level might play a important role here.

However, the ranking of competitiveness does not change much from 1990 to 2005. Japan is still

the country with strongest competitiveness, followed by USA and Germany. The country within

the group with the least competitiveness is still Greece. If we run the regression for the whole

sample, the result is given in Table 6.

[Table 6 Here]

Note that the values in Table 6 are the relative competitiveness of the countries. Within the

OECD group, the rank is consistent with previous estimation. Japan is still the OECD country

with the strongest competitiveness, followed by USA and Germany. Some newly joined OECD

members, such as South Korea, Poland and Turkey also have relatively high competitiveness. The

most important �nding is that the BRIC countries (Brazil, Russia, India and China) have rather

If we do not impose such a restriction, the estimated elasticity of trade is 5.63, with a standard error of 0.11. The

estimation result is still signi�cantly less than 6.10, the result from pooled sample.22 If we use the log of distance instead of these distance dummies, the estimation result for other variables do not

change much.

24

high competitiveness, even compared with most OECD members. This is reasonable, as the BRIC

countries all have large population and technology level which is comparable to the developed world.

Within them, China has the strongest competitiveness among all countries. With huge population

and not too lack-behind technology level, no wonder China will become the "world factory" in

recent years, especially after its accession to WTO in 2001, which makes it more integrated with

the other countries in the world.

To take into account of fragmentation, we re-estimate using the newly available TiVA (Trade

in Value Added) data. This dataset addresses the double counting implicit in current gross �ows of

trade, and instead measures �ows related to the value that is added (labour compensation, taxes

and pro�ts) by a country in the production of any good or service that is exported. For example, if

country A exports $100 of goods, produced entirely within A, to country B that further processes

them before exporting them to C where they are consumed. B adds value of $10 to the goods and

so exports $110 to C. Conventional measures of trade show total global exports and imports of

$210 but only $110 of value-added has been generated in their production. Conventional measures

also show that C has a trade de�cit of $110 with B, and no trade at all with A, despite the fact

that A is the chief bene�ciary of C�s consumption. If instead we track �ows in value-added, C�s

trade de�cit with B reduces to $10 and it now runs a de�cit of $100 with A. We use this adjusted

trade volume in value-added, which is exactly the X 0ml we described in equation (12). We also use

the modi�ed version of trade shares as following

X 0nl

Xn=

TiVAnlTotal Value Addedn � Total TiVA Exportsn + Total TiVA Importsn

(15)

X 0nn

Xn= 1�

Xl 6=n

X 0nl

Xn(16)

After this adjustment, we run the regression of equation (12) and get result in Table 7.

After Adjustment All Countries OECD Countries Non-OECD Countries Other Pairs

Estimation of � (year 2005) 5.81 (0.06) 5.76 (0.17) 6.20 (0.10) 5.48 (0.08)

Table 7: Estimation using TiVA and the ICP 2005 data

Compared with the result based on gross trade volume in Table 4, it is clear that the estimate

of trade elasticity � is distinctly smaller for the OECD group, which is consistent with the theory

we have proposed. Note that though the magnitude of the elasticities do not seem to di¤er that

much after the adjustment, the estimates in both Table 4 and 7 are statistically signi�cant at 1%

level. Moreover, the usual estimation result of higher elasticity of trade among Northern countries

does not hold after the adjustment. The change in the estimates of elasticity of trade among Non-

OECD countries is not as clear. The reason is like what we describe before, for some large Southern

countries, other Southern countries may serve as assembling centers. As there is overcounting and

25

under-counting at the same time, the e¤ect is mixed. When we carry out the same regression

based on trade in value-added between the Southern assembling centers and their corresponding

(OECD) partner countries as before, the estimated elasticity of trade is 5:99, with a standard error

of 0:12.23 The estimate is higher than both the estimate for All Countries (5.81) and that for

the OECD Countries group (6.20). Comparing with the ranking of the estimated trade elasticity

using gross trade data, we can see that the ranking of the estimated trade elasticity is reversed

when trade in value-added data are used. Northern countries are usually both the suppliers of

intermediate goods and the destinations of the �nal goods due to their large technology stocks

and economy sizes. Thus our model predicts a lot of �missing trade� of value-added among the

Northern countries when a Southern country serves as the assembling center for them. Gross trade

data therefore understate North-North trade, leading to a higher estimated elasticity of trade. On

the other hand, gross trade data overstate trade between the assembling centers and their Northern

partners, leading to a lower estimated elasticity of trade. The above results are totally consistent

with our theory, which implies that international fragmentation is the main driving force for the

asymmetry between the North and the South when one estimates the gravity model. However, our

model cannot fully explain why the estimated elasticity of trade gets smaller for the pooled sample

of North-South and South-North trade (Other Pairs) after adjustment (a fall from 5.77 to 5.48).

A possible reason is that there are larger volumes of exports of raw materials from some Southern

countries to the North. This is not documented in the current set of TiVA data.

It will be more interesting for us to look at the estimation which also captures the country �xed

e¤ects. We re-estimate Table 5 with TiVA data and obtain Table 8. It is clear that for the OECD

group, whether the estimation is based on gross trade volume or trade in value-added does not

make much di¤erence here. All the estimates are similar in magnitude. However, the di¤erence in

Si is even smaller, which indicates that the competitiveness of the OECD countries are even more

similar to each other than we thought based on gross trade volumes. Also, after the adjustment,

the competitiveness of USA is now slightly higher than Japan, making it now the most competiitve

country in OECD group. The reason may be that as Japan is the only OECD country in Asia, it

is responsible for the �nal production of some high-tech product for neighboring countries. While

it imports intermediate parts from other OECD countries, like USA, Germany and Britain, and

reexport the �nal product to nearby countries, like China, there is also double-counting in gross

trade compared with trade in value-added. As a result, the competitiveness of Japan is slightly

overestimated.

[Table 8 Here]

[Table 9 Here]

23 If we do not impose such restriction, the estimated elasticity of trade is 6.29, with a standard error of 0.09.

26

If we re-estimate for the entire sample, the result, which are shown in Table 9, seems more

interesting. Although China is still the country with the strongest competitiveness, the magnitude

of its competitiveness shrink a lot compared with Table 6. China is also not the only country with its

competitiveness over-estimated. For many developing countries, like China and ASEAN countries,

the competitiveness have been strongly overestimated. At the same time, the competitiveness of the

Northern countries show no signi�cant change or are underestimated. This pattern is consistent

with our theory that the competitiveness of the assembling centers are overestimated as their

export volume is magni�ed by the "back-and-forth" trade; while the competitiveness of the source

countries are underestimated as their export volumes are wrongly attributed to the assembling

centers. Another interesting �nding is that, unlike those of the Asian assembling centers, the

competitiveness of the Central European countries have not been overestimated in general. The

possible reason might be they mainly trade with EU partners and the economy size of each of them

is not large.

3.3 Robustness Check Using EIU Price Data

For robustness check, we carry out the same empirical analysis as in subsection 3.1 and 3.2 using

Economist Intelligent Unit (EIU) Worldwide Retail Price Survey24 of year 2000 and 2005. The

bilateral trade volume and domestic production data are from the same data source as the above

exercise. The EIU survey gathers detailed information on the cost of more than 160 items most

related to daily living in 123 major cities from 79 countries. The items are covering daily goods or

serve from the following 13 categories, Shopping basket, Alcoholic beverages, Household supplies,

Personal care, Tobacco, Utilities, Clothing, Domestic help, Recreation & entertainment, Trans-

portation, Housing rents, International schools, health & sports and Business trip costs. Price

of many goods are collected at both supermarket and mid-price store level, a total of 304 data

points are gathered for each city. Among them are 214 tradable goods, which are included in our

calculation. The cities are usually the capital, largest city or the largest port of the countries.

Big countries like USA, UK, Germany and China includes multiple cities. We �rst follow EK and

Waugh (2010) to construct b� cd = max 3i

pc (i)

pd (i)

for each pair of cities (c; d) among all 214 categories (i), where max 3 denotes the third highest

value. This gives estimated trade costs for each pair of cities, the third largest value is chosen

to avoid possible measurement error in the prices for particular commodities.25 For each country

pair, which potentially contains multiple city pairs, we use the lowest value of b� cd to stand for24The website is http://www.worldwidecosto�iving.com/asp/wcol_WCOLHome.asp. Subscription is required to

access to the data.25This is the same reason as Eaton and Kortum (2002). The price of many goods are available at 2 levels of stores.

Thus we choose the third largest value.

27

the trade costs between countries, as we really want to measure the trade costs across countries

rather than within the countries. For example, the 16 USA cities and 8 Chinese cities form 128 city

pairs for China-USA trade costs, and we use the minimum of the 128 b� cd to represent it. Thereare several advantages of the data. First, the goods it looks at are very detailed goods, like white

bread, or toothpaste, even coca-cola, we are really comparing the exactly same goods, or even the

same brand other than price indexes in ICP. Second, the price data is collected at each city, which

leads to a more accurate estimation of trade cost, compared with a aggregate price index for the

whole country. Third, the category and country coverage is fairly close to the ICP benchmark data.

There is also a clear disadvantage that only daily goods are considered. Large manufactory goods,

like equipment are ignored from the data.

After obtaining the necessary data, we run the OLS regression following equation (12), with Sl

as �xed e¤ect for importers and Sm as �xed e¤ect for exporters. We also run the regression for the

pooled data, OECD subgroup, non-OECD subgroup and cross OECD and non-OECD subgroup

respectively. The results are as following

All Countries OECD Countries Non-OECD Countries Other Pairs

Estimation of � (year 2000) 3.404 3.759 3.805 3.121

Estimation of � (year 2005) 3.622 3.978 3.776 3.177

Table 10: Estimation using the EIU data

Similar to what we observe using the ICP price data, the within-OECD estimation is distinctly

higher than overall estimation of �, and the result for North-South and South-North trade is lower

than the overall estimation. The estimations are also within the range of estimation by Simonovska

and Waugh (2013). Using more recent disaggregate price (ICP 2005) and trade-�ow data and

developing a SMM method, they obtain the estimation of � to be between 2:54 and 4:42. They also

use the EIU price data for robustness check at the end of the paper, which yield lower estimation

compared with the ICP data. This explains the di¤erences between the estimates of � using di¤erent

data resource. Simonovska and Waugh (2013) also aggregate the EIU data in the manner of ICP

and still get quite di¤erent result compared with the results from the ICP data. This might be

caused by certain systematic di¤erence between these two dataset. Thus we do not try similar

aggregation here. We also do not tend to compare these two price data. We only want to show the

e¤ectiveness of our adjustment. Here we carried out the same adjustment based on TiVA data as

described above and rerun the regression of equation (12). The result is as following

After Adjustment OECD Countries

Estimation of � (year 2000) 3.402

Estimation of � (year 2005) 3.611

Table 11: Estimation after adjustment using the EIU data

28

For di¤erent time period and di¤erent data resource, the estimation of trade elasticity for the

OECD countries tends to be very close to the estimation for all countries. These �ndings con�rm

our conjecture that the miscounting for the back-and-forth trade between North and South caused

by fragmentation is in fact the driven force for the systematic asymmetry between Northern and

Southern countries in global trade, especially in recent years.

4 Other Implications

The model also has some other implications for existing trade data. We can propose a conjecture

to explain the zeros in bilateral trade �ows and also related the import-to-export ratio documented

by custom data to the relative technology stock (comparative advantage) of each pair of countries

for di¤erent industries.

4.1 Zeros in Bilateral Trade Flows

Many researchers are also puzzled by the zeros in bilateral trade �ows and try to explain it using

various methods. Advanced econometric method and usually complicated models are introduced to

solve for the problem. Helpman, Melitz, and Rubinstein (2008), Eaton, Kortum and Sotelo (2011)

and Armenter and Koren (2012) are all good attempts to the question. However, they may have

ignored the e¤ect of the changing nature of trade. These zeros are possibly results of fragmentation.

In order to �t the complicated real world, we relax our assumptions here.

Following Eaton & Kortum (2006), we allow for a common technology stock TC to be shared

by Northern and Southern countries. We assume that technology di¤usion from the common

technology pool TC is the only resource for South to obtain technology.26 Also, if the technology

is already obtained by the assembling center, Northern countries will use their extra technology

to produce in fragmentation. There are heterogeneity in the speed of technology di¤usion, as

documented by Comin and Hobjin (2010). Thus the technology stock still di¤ers across Southern

countries. There are two types of goods, new goods with TC = 0, for which only North can produce,

and old goods with positive TC . All goods enter the demand. Thus in equilibrium, only North

produce the new goods and export it to all the other countries. The assembling of the old goods

can be o¤shored to a Southern country. However, only countries with larger technology stock will

supply the intermediate inputs. The assembling center counties will assemble the intermediate

inputs, both domestic and imported, to the �nal goods and export it to countries are not too far

away. Under this simply setting, the predict trade pattern for countries will be as following:

26This assumption seems strong, but is consistent with the reality that the few North countries are the major

provider of technology all over the world.

29

1. Northern countries will export everywhere, but they will not import from the non-assembling-

center Southern countries.

2. Southern assembling center countries will only import from countries with higher technology

stock, but export to countries within certain distance.

3. Southern non-assembling-center countries will import from Northern countries and assembling

centers, but not export.

In the following, we use the aggregate bilateral trade �ows (in U.S. Dollars) of manufactures of

year 1992 from Feenstra, Lipsey, and Bowen (1997), document the zeros and divided all the 92 coun-

tries in the dataset into 3 groups: OECD countries, emerging markets and other countries.27 Each

group represents Northern countries, Assembling Center Southern countries and non-assembling-

center Southern countries respectively. This is de�nite not a perfect match. But certain pattern

can be clearly seen from it.

Zeros as Exporter Zeros as Importer

OECD (19) 1:37(3:52) 8:16 (8:85)

Emerging Markets (21) 9:67(9:30) 23:05(7:05)

Others (52) 51:15(14:06) 43:23(9:27)

All (92) 31:40(25:54) 31:40(16:84)

Table 12: Zeros in bilateral trade

The above table documents the mean and standard deviation of the zeros in bilateral trade �ows,

for countries both as exporters and importers. The pattern is consistent with the prediction of our

model. However, our prediction clearly overestimate some of the zeros, especially for the zeros as

importer for the �rst group and zeros as exporters for the last group. For the OECD countries, our

simply model predicts that they will not import from countries in last group, but the average of

zeros is just 8:16. Meanwhile, the model predicts that the last group will not export, but the average

of zeros is 51:15 rather than 91. The reason for this is that, there is also dispersion of technology

capacity across goods in reality, which is largely ignored here in our simply model. Countries in the

last group will not usually serve as assembling center. But they may has reasonable high technology

stock in certain goods, such that they can serve as the assembling center, or intermediate input

provider of those goods. As a result, they may export those goods (at least parts of the goods).

This complexity is clearly beyond the ability of our simply model here.

27OECD countries only consist of those countries joins OECD before 1992. If a country is classi�ed as emerging

market, either by IMF, or MSCI Barra, we put it into second type. All the other countries goes to the third type.

30

4.2 Relation to Import-to-export Ratio

The world seems to be more complicated if measure of assembling � > 0. It might be disappointing

to see such a measurement bias in the gravity equation induced by the back-and-forth trade.

However, the model allows us to deal with data at more disaggregate level, and reveals parameters

which is normally hard to measure in practise.

All above analysis in fact apply to the production of a typical good i. As we previously discussed,

the "back-and-forth" trade in China can be mostly captured by processing trade. China has served

as a assembling center in these processing trade. For the assembling country n and each good i, it

import goods with value of knmpni from each countrym, the total import sum up to be (1� knn) pniper unit. Meanwhile, the unit price of export is Pmi = pni

�1 + �k

� 1�

nn

�. Thus the import-to-export

ratio for each good is(1� knn) pni

Pni=

1� knn1 + �k

� 1�

nn

which is a function of the measure of tasks carried by country n, knn, and decrease with knn as

long as knn is not too small.28 The ranking of import-to-export ratio reveals a reverse ranking of

knn =Tni(cn)

��

�ni, a measure of China�s relative technology stock in producing this good, compared

with the rest of the world.

In a recent empirical study, Kee & Tang (2012), the authors have focused on the domestic

value added (DVA) ratio, which is 1� import-to-export ratio in our model. They investigate the

processing export for �rms that only operate within each 2-digit HS industry, based on the Chinese

custom data. In their paper, they �nd out that there is substantial growth in the DVA ratio of

Chinese processing trade exporters. The e¤ect is not driven by rising cost of Chinese workers, but

substitution towards domestic intermediates. The e¤ect also varies across di¤erent ownership of

the �rms. Surprisingly, the state-owned enterprises (SOEs) in average has a similar magnitude of

DVA ratio, compared with private �rms. But the foreign-owned �rms usually has a larger domestic

value added than domestic private-owned �rms. For the year by year increase in DVA ratio, it also

does not show much di¤erence between SOEs and private �rms, but favors the foreign-owned �rms

except for the �rst year (year 2001, just after China joins the WTO).

Those empirical �ndings can be well explained by our model. The fast increase in domestic

value added ratio (or decrease of import-to-export ratio) of Chinese �rms in recent years is mainly

driven by the increased technology stock through di¤usion from other countries. Eaton & Kortum

(2009) has shown that although the increase in China�patent abroad from 1995-1997 to 2003-2005

is negligible29, the increase in foreign patenting in China is substantial. In years 1995-1997, only

1441 foreign initiated patents have been issued in China, the number boom to 28007 in years 2003-

28When � is small, the import-to-export ratio is roughly 1� knn.29 It increases from 135 to 658 from year 1995-1997 to year 2003-2005, compared with the 46103 and 62734 for U.S..

31

2005, which is comparable with the number of Japan and Germany at the same period. The 20

times increase in less than a decade makes massive technology di¤used to China, which increase

knn for China. Thus the domestic value added ratio also increases. In fact, the slightly increase

in labor cost will have the opposite e¤ect. As China weakens its comparative advantage along

the production line by higher labor cost, fewer tasks will be carried in China, other than the �nal

assembling. No wondering the e¤ect of wage on domestic value added ratio is not signi�cant, and

with a negative sign in the reduced form regression carried by the authors.

We can also decompose the e¤ect by �rm type. For the SOEs, they can pursue technology with

the support and aids from the government and foreign-owned �rms can obtain advanced technology

from its mother company directly. Private-owned �rms has no such ability, thus the technology

adopted is less and slower. As a result, they will have a lower and slower growing knn, and thus a

lower domestic value added ratio. The boom in 2001 can be rationalized by the removed restriction

of foreign investment and better patent protection after China joins the WTO. Private-owned �rms

might obtain technology from the SOEs and Foreign-Owned �rms at the beginning. But this

channel is much less e¢ cient in the following years. Another interesting �nding for the domestic

value added ratio is that, there is a signi�cant drop in year 2004. We will try to explain it in the

next section, considering the general equilibrium e¤ect of the two-country model.

The import-to-export ratio is not the only relevant parameter. For good i, n = China is the

assembling center, the import shares of two di¤erent countries l and m also give information on

relative technology stock of those countries. For good i�knlknm

�i

=TliTmi

��cl�nlcm�nm

���is proportion to the relative technology stock of these two countries in producing good i. Tli

Tmi<

TljTmj

,�knlknm

�i<�knlknm

�j, the import share ratio gives a perfect rank and good proxy of countries�

comparative advantage in production technology.

5 Conclusion and Remarks

In this paper, we develop a multi-country Ricardian model of comparative advantage with inter-

national fragmentation of production by modifying the Eaton and Kortum (2002) framework. We

show that international fragmentation of the production process has important implications. First,

it explains the "triangular trade" between countries in the global trading system, and predicts the

locations of the assembling centers. Second, using the gravity equation derived in the benchmark

(� = 0) case, we show that under normal circumstance, the gravity equation based on the original

Eaton-Kortum model, which does not account for back-and-forth trade, yields higher estimated

e¢ ciency dispersion parameter (trade elasticity) for Northern countries compared with other coun-

32

tries. This result is con�rmed empirically. Third, we adjust for back-and-forth trade by using the

newly published trade in value added (TiVA) data released by the OECD in May 2013. We �nd that

after this adjustment the observed systematic asymmetry in the estimated trade elasticity between

North and South diminishes substantially. Fourth, the estimation result reveals strong bias in the

estimation of countries�competitiveness if the fragmentation feature is ignored. Fifth, our model

can also explain the zeros in bilateral trade �ows. We therefore suggest that, to better account

for the e¤ect of fragmentation on global trade, countries should collect data on where intermediate

goods come from and where �nal goods go to, corresponding to each �nal good category. The

TiVA dataset is complied based on this spirit, but the data are still just estimations, rather than

statistics. Governments and international organizations can possibly make the measurements of

trade in value-added more accurate. It fact, our empirical analysis can be applied to an individual

industry, with the intermediate inputs possibly coming from other industries, when more accurate

disaggregate data on trade in value-added is available.

An important contribution of this paper is that it reveals not only the importance of frag-

mentation of production, but also how the respective role of each country is determined in the

fragmentation process. Researchers who ignore these features might end up with biased results

and estimations. Because of existence of such shortcoming in measuring bilateral trade �ows, the

omission of fragmentation can lead to biases in many empirical studies that make use of bilateral

trade �ows, not just in the estimations in gravity models. For example, after taking fragmenta-

tion into consideration, the USA-China trade de�cit might be much smaller than people usually

think. For future research, we can extend the model to incorporate technology di¤usion, structural

change, trade imbalance, etc. In particular, if multi-country technology creation and technology

di¤usion can be incorporated into our model, it can become a dynamic model of technological

change, di¤usion and trade that can be estimated empirically.

33

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36

Appendix

A Proof of Proposition 1

The equation (6) is equivalent to

XN

m=1�ml

k1+ 1

�ml

k1�mm

Lm = Ll;8l

It is noteworthy that all the fraction of intermediate tasks, kml are functions of {cl} once the set

of technology {Tl} and trade costs {�ml} are known. Furthermore, we can easily verify that

@kml@cl

< 0 and@kml@cn

> 0, 8n 6= l

Thus the LHS of equation (6) will decrease while cl increases and will increase while cn (n 6= l)

increases. Then the above system has a unique solution if we pick up a country as a benchmark

and use its labor cost as numeraire.

B The Derivation for the 2-Country Case

1. When � = 0

In the costless assembling world,

LAkAA + �LBT

1�B

T1�A

k1+ 1

�BA

k1�BB

= LA

LAkAA + �LBT

1�B

T1�A

k1+ 1

�BA

k1�BB

= LA

) LAT1�A

LBT1�B

=�k

1+ 1�

BA

kABk1�BB

(17)

=kBAk

1�AA

�k1+ 1

�AB

(18)

As kAA, kBA decreases withcAcB, kAB, kBB increases with cA

cB, the RHS of equation 17 de-

creases with cAcB. When the competitiveness of a country increases due to population growth,

the relative wage of that country will decrease. At the same time, the tasks the country

perform becomes more, thus real wage cApA= 1

�(1+ 1� )

�TAkAA

� 1�also decrease. If the increase in

competitiveness is due to technology upgrading, kBAkBBTA

will not be a¤ected. As kBA increases

while kAB decreases, relative wagecAcBhas to increase to restore the equilibrium, the real wage

cApAwill increase as well.

37

2. When � > 0 and each country assembles its own �nal consumption

In this situation, labor market clearing leads to

LAk1+ 1

�AA

k1�AA + �

+ �LBT

1�B

T1�A

k1+ 1

�BA

k1�BB + �

+ �LA

k1�AA + �

= LA

Rearranging it, we will have

LAT1�A

LBT1�B

=

�

�k1�AA + �

�k1+ 1

�BA�

k1�BB + �

�kABk

1�AA

(19)

,which is parallel to equation (17) of the costless assembling case.30 As before, we use Di =

LiT1�i (i = A;B) to stand for the competitiveness of each country i. If the two countries have

the same level of competitiveness, DA = DB, above equation leads to kAA = kBB = 11+���

,

no matter how large � is.31 In this case, TAc��A = TBc

��B , then

cAcB=

�TATB

� 1�

=

�TA=LATB=LB

� 1�+1

To sum up, with LAT1�A = LBT

1�B , we will have the same relative wage, the same measure of

intermediate tasks as the costless assembling world. The only di¤erence is the real wage

ciPi=

1

��1 + 1

�

� T1�i

k1�ii + �

which is smaller.

When these two countries have di¤erent competitiveness, e.g. DA > DB, then kAA > 11+���

>

kBB due to monotonicity. When � increases, it is easy to check that the RHS of equation (19)

will increase. Under the original kAA, we have RHS > LHS, thus kAA decreases as a result.

kAAkBA

and kABkBA

will also decrease, which leads to k1�AA+�

k1�BB+�

increases and k1�AA + � increases. As a

result cAPA= 1

�(1+ 1� )

T1�A

k1�AA+�

decreases. For the country with stronger competitiveness, larger �

re�ects the fact that it will spend more labor on the less productive assembling process, which

lowers the average productivity and make the workers worse o¤. However, the welfare e¤ect

on the workers in the less competitive country will be the opposite. If we do not change � but

enhance the competitiveness of country A, the increase in LHS of equation (19) will lead kAA

to increases. If the increase in DA is caused by population growth, then It is clear that both

30With symmetry, it is easy to show that above relationship applies to the case with mutiple countries with

symmetric trade costs when each country serves as its own assemblng center.31When � = 0, eqution (19) will degenerate to equation (17), kAA = kBB = 1

1+��� will still be the solution while

DA = DB.

38

the relative wage cAcB and real wagecAPAwill decrease. But if the increases in competitiveness is

induced by technology upgrading, the relative wage will increase, and the increase in k1�AA+�

will clearly be less than increase in T1�A , real wage

cAPAalso increase.

3. When � > 0 and country A assembles all the goods

Now we suppose that the competitiveness of the country A keeps to increase, then kAA will

continue to go up, until each country assembles its own consumption cannot be a equilibrium,

The country B�s consumer will be indi¤erence between the two possible assembling centers

when

PA� = PB

, �2k1�BA(1 + �k

� 1�

AA) = k1�BB(1 + �k

� 1�

BB)

In this case, some of country B�s consumption might be assembled in country A, and the rest

will be assembled domestically. If DA increases even further, we will have �2k1�BA(1+�k

� 1�

AA) <

k1�BB + �, which is equivalent to PA� < PB. Then all the goods will be assembled in country

A.

In this case, the labor market clearing is that

LAk1+ 1

�AA + �

k1�AA + �

+ �LBcBcA

k1+ 1

�AA + �

�

�k1�AA + �

� = LA

�LAT

1�A

T1�B

k1+ 1

�AB

k1�AA + �

+ LBcBcA

�2k1+ 1

�AB

�

�k1�AA + �

� = LB

which leads toLALB

=cBcA

k1+ 1

�AA + �

k1�AAkAB

When cAcBincreases, kAA decreases and kAB increases. The RHS of above equation decreases

with cAcB. The larger population will lower down the relative wage and the real wage of the

country as well. Thus we can draw the following �gure to describe the the relationship

between LA=LB and cA=cB under this special case.

39

Data Description

To empirically test the theories we proposed in the model, we use data from various sources.

In the next, we provide a simply summary of the data we use in the paper

� Bilateral trade volume is from the PC-TAS (Trade Analysis system on Personal Computer)

from the International Trade Centre. This dataset includes both the reports of bilateral trade

volume from the exporters and the importers, which stand for the value based on f.o.b. and

c.i.f. prices respectively. We use the exporter�s report while identifying the assembling centers,

to avoid the possible upward bias (the gross trade volume reported from the importers are

in general higher, then it possibly magni�es the di¤erence between gross trade volume and

trade in value added). For the gravity estimation, we adopt the importers�reported value

as it will be comparable with the �nal consumption at each destination. We also follow the

method proposed by Head, Mayer & Ries (2010) to clean for the unconventional values.

� Measuring Trade in Value Added (TiVA) data, an OECD-WTO joint project to back up thevalue that is added by a country in the production of any good or service that is exported

to the destination country. This data source is published in late May 2013, which completely

coincides our paper in spirit. We also believe that we are the �rst one upon researchers to

apply this data to the gravity equation practise.

� Disaggregated price data from the International Comparison Program (ICP) 2005 round.

The ICP price data covers 123 countries, and it collects price data on goods with identical

characteristics across retail locations in the participating countries during the 2003-2005 pe-

riod. The data set contains a total of 129 basic headings, and the 62 tradable goods are

employed for our estimation of trade costs. Following the method proposed by Eaton & Ko-

rtum (2002), we use this dataset to estimate for the trade costs and aggregate price index of

each country.

� GDP per capita from Penn World Table (PWT) 7.1 is used to proxy for the wage level of

each country. As year 2005 is set as the reference year in this version, the data accuracy is

assured.

� Both the number of patent and average schooling years of residents are used as proxy foreach country�s technology stock. The former comes from the OECD Patent Statistics, which

includes statistics on patent counts by regions where EPO and PCT �lings are presented

according to the region of the inventors/applicants residence. The latter comes from Interna-

tional Human Development Indicator of the UN, in which they update Barro and Lee (2011)

estimates based on UNESCO Institute for Statistics data on education attainment (2012) and

Barro and Lee (2010) methodology.

40

� Gross manufacturing production of each country, which is usually the major data obstacle forgravity estimation with multiple countries, directly comes from the International Yearbook

of Industrial Statistics of year 2008 to 2012 in this paper. To be consistent, we only take

the number documented for year 2005. If the number is available in the yearbooks of various

years, we adopt the latest available number as the accurate one.

� Other gravity-related measurements of trade for each country pair, e.g. distance, sharedborder, shared language, whether a regional trade agreement (RTA) exists, are adopted from

the GeoDist and Gravity dataset of the CEPII website.

We tend to adopt all above data in their raw status, in order to avoid any possible bias caused

by inappropriate treatment.

41

Tables

Table 1: Gross Export and TiVA Export for Large Developed and Developing Countries in 2005

Country Total Export (billion $) Share in Global Trade TiVA Export Share in Global TiVA

Germany 977.13 9.6% 691.17 8.5%

USA 904.34 8.9% 945.31 11.6%

Japan 594.94 5.9% 534.23 6.6%

France 434.35 4.3% 394.44 4.9%

UK 384.36 3.8% 421.08 5.2%

Italy 372.96 3.7% 327.36 4%

Canada 360.55 3.6% 305.37 3.8%

Netherlands 349.81 3.5% 195.75 2.4%

Belgium 334.10 3.3% 122.87 1.5%

Hong Kong 292.12 2.9% 57.01 0.7%

China 761.95 7.5% 499.03 6.1%

Russia 241.45 2.4% 238.94 2.9%

Mexico 214.21 2.1% 150.28 1.9%

Malaysia 141.62 1.4% 90.13 1.1%

Brazil 118.53 1.2% 115.12 1.4%

Thailand 110.11 1.1% 76.07 0.9%

India 100.35 1.0% 123.52 1.5%

Indonesia 85.66 0.8% 76.49 0.9%

South Africa 47.00 0.5% 53.90 0.7%

Table 2 : Direct Testing of Proposition 2

Whole Sample Dropping Port Countries

Variable Logit OLS Logit OLS

ln(trade cost) �� -1.70��(0.13) -0.87��(0.06) -1.74��(0.14) -0.87��(0.06)

ln(relative wage) �C -0.26��(0.04) -0.14��(0.02) -0.39��(0.05) -0.19��(0.02)

ln(relative # of patents) �P 0.04�(0.016) 0.04��(0.007) 0.07��(0.02) 0.05��(0.008)

ln(relative years of schooling) �H 0.55��(0.18) 0.33��(0.08) 0.79��(0.19) 0.43��(0.09)

� indicates 5% signi�cant level, �� indicates 1% signi�cant level

42

Table 3 : Price Measure Statistics for OECD Countries

Foreign Sources Foreign Destinations

Country Minimum Maximum Minimum Maximum

Australia (AUS) GBR(1:46) USA(3:32) FIN(1:50) USA(2:75)

Austria (AUT) BEL(1:26) CAN(3:55) DEU(1:23) JPN(2:32)

Belgium (BEL) FRA(1:22) CAN(3:05) AUT(1:26) JPN(2:25)

Canada (CAN) BEL(2:01) JPN(3:28) FIN(2:22) JPN(4:45)

Denmark (DNK) FIN(1:39) CAN(2:97) SWE(1:33) JPN(2:67)

Finland (FIN) NOR(1:37) USA(2:69) DNK(1:39) JPN(2:90)

France (FRA) AUT(1:39) CAN(3:22) BEL(1:22) JPN(2:31)

Germany (DEU) AUT(1:23) CAN(3:66) AUT(1:27) JPN(2:40)

Greece (GRC) ITA(1:41) USA(2:52) PRT(1:46) JPN(2:83)

Italy (ITA) FRA(1:37) CAN(3:54) BEL(1:32) JPN(2:74)

Japan (JPN) AUS(2:02) CAN(4:45) ITA(2:05) CAN(3:28)

Netherlands (NLD) DNK(1:39) CAN(4:27) BEL(1:50) JPN(2:56)

New Zealand (NZL) SWE(1:40) CAN(3:92) FIN(1:57) JPN(3:22)

Norway (NOR) GBR(1:50) CAN(3:75) FIN(1:37) JPN(2:56)

Portugal (PRL) ESP(1:30) CAN(2:85) ESP(1:44) JPN(3:18)

Spain (ESP) BEL(1:34) USA(2:76) PRT(1:30) JPN(2:63)

Sweden (SWE) DNK(1:33) CAN(3:04) BEL(1:37) JPN(3:24)

United Kingdom (GBR) FRA(1:45) CAN(3:00) AUS(1:46) USA(2:46)

United States (USA) DEU(1:82) CAN(3:23) CAN(2:25) JPN(3:83)

43

Table 3a : Price Measure Statistics for New OECD Countries

Foreign Sources Foreign Destinations

Country Minimum Maximum Minimum Maximum

Chile (CHL) EST(1.88) BRA(2.96) MLT(2.01) SGP(5.38)

Czech Republic (CZE) POL(1.35) SAU(3.90) SVK(1.32) VNM(3.93)

Estonia (EST) LTU(1.35) SAU(3.35) LVA(1.3) VNM(4.27)

Hungary (HUN) CZE(1.32) SAU(4.34) LTU(1.38) JPN(3.93)

Iceland (ISL) NOR(1.31) RUS(4.81) FIN(1.31) VNM(5.23)

Ireland (IRL) GBR(1.38) RUS(6.04) LUX(1.34) VNM(4.52)

Israel (ISR) SVN(1.55) SAU(4.06) HUN(1.55) VNM(3.41)

South Korea (KOR) ITA(2.04) USA(4.57) LVA(1.74) VNM(5.71)

Luxembourg (LUX) AUT(1.3) USA(3.37) BEL(1.34) VNM(5.58)

Mexico (MEX) IRL(1.56) HKG(2.98) BGR(1.49) VNM(3.61)

Poland (POL) LTU(1.32) KHM(4.1) SVK(1.33) JPN(4.43)

Slovak Republic (SVK) CZE(1.32) SAU(4.27) CZE(1.36) SGP(4.56)

Slovenia (SVN) BEL(1.31) SAU(3.68) ESP(1.34) VNM(4.71)

Switzerland (CHE) BEL(1.52) ARG(4.11) LUX(1.32) VNM(6.47)

Turkey (TUR) HUN(1.73) SAU(5) BGR(1.66) VNM(3.34)

44

Table 3b : Price Measure Statistics for Non-OECD Countries

Foreign Sources Foreign Destinations

Country Minimum Maximum Minimum Maximum

Argentina (ARG) BRA(1.65) JPN(3.44) ROM(1.88) SGP(4.66)

Brazil (BRA) CHN(1.66) KHM(5.43) ARG(1.65) SGP(4.36)

Brunei (BRN) HKG(1.62) IND(3.59) THA(1.69) VNM(4.23)

Bulgaria (BGR) HUN(1.40) SAU(4.41) POL(1.45) JPN(3.94)

Cambodia (KHM) CAN(1.46) BRA(3.07) CAN(1.50) SGP(5.46)

China (CHN) EST(1.70) KHM(3.28) BRA(1.66) VNM(4.59)

Chinese Taipei (TWN) HKG(1.42) SVK(3.74) THA(1.65) VNM(3.52)

Hong Kong (HKG) AUS(1.77) SAU(5.88) TWN(1.42) VNM(3.63)

India (IND) THA(1.6) SAU(4.52) THA(2.05) SAU(4.08)

Indonesia (IDN) THA(1.71) JPN(5.06) PHL(1.72) JPN(2.80)

Latvia (LVA) LTU(1.28) SAU(3.62) LTU(1.23) VNM(3.76)

Lithuania (LTU) LVA(1.23) SAU(3.76) LVA(1.28) JPN(3.70)

Malaysia (MYS) SGP(1.46) AUT(4.63) THA(1.61) JPN(3.38)

Malta (MLT) HUN(1.45) HKG(3.04) RUS(1.58) VNM(3.53)

Philippines (PHL) TWN(1.67) SAU(3.57) THA(1.74) KOR(3.42)

Romania (ROM) HUN(1.48) SAU(3.82) LVA(1.44) JPN(4.19)

Russia (RUS) LVA(1.51) JPN(2.84) LVA(1.50) SGP(6.33)

Saudi Arabia (SAU) BRN(1.83) SVK(4.54) BRN(1.83) HKG(5.88)

Singapore (SGP) THA(1.82) RUS(6.33) MYS(1.46) POL(3.16)

South Africa (ZAF) MEX(1.64) KOR(3.76) EST(1.72) VNM(3.93)

Thailand (THA) MYS(1.61) KHM(3.43) IND(1.60) KOR(4.18)

Viet Nam (VNM) IDN(1.82) JPN(9.20) BGR(1.65) AUS(3.27)

45

Table 5 : Bilateral Trade Equation for OECD Countries

Variable est. s.e.

Distance [0,375) -�d1 -2.12 (0.71)

Distance [375,750) -�d2 -2.77 (0.81)

Distance [750,1500) -�d3 -3.54 (0.76)

Distance [1500,3000) -�d4 -4.37 (0.76)

Distance [3000,6000) -�d5 -5.01 (0.64)

Distance [6000,maximum) -�d6 -5.52 (0.13)

Shared border -�b 0.46 (0.23)

Shared language -�l 0.84 (0.19)

RTA -�f -0.06 (0.43)

Country est. s.e.

Australia S1 -0.52 (0.14)

Austria S2 -0.40 (0.14)

Canada S3 -0.15 (0.14)

Denmark S4 -0.69 (0.14)

Finland S5 -0.31 (0.14)

France S6 0.79 (0.14)

Germany S7 1.11 (0.14)

Greece S8 -1.23 (0.14)

Italy S9 0.87 (0.14)

Japan S10 1.53 (0.14)

Netherlands S11 -0.46 (0.14)

New Zealand S12 -1.00 (0.14)

Norway S13 -0.82 (0.14)

Portugal S14 -0.71 (0.14)

Spain S15 0.31 (0.14)

Sweden S16 -0.08 (0.14)

United Kingdom S17 0.38 (0.14)

United States S18 1.36 (0.14)

46

Table 6 : Estimation of Competitiveness

Country est. s.e. Country est. s.e.

AUT S1 0.09 (0.13) JPN S23 2.01 (0.13)

BGR S2 -1.30 (0.13) KOR S24 1.48 (0.13)

BRA S3 1.06 (0.13) LTU S25 -1.70 (0.13)

CAN S4 0.24 (0.13) LVA S26 -2.26 (0.13)

CHE S5 0.24 (0.13) MEX S27 -0.49 (0.13)

CHL S6 -0.21 (0.13) MYS S28 -0.05 (0.13)

CHN S7 2.23 (0.13) NLD S29 -0.17 (0.13)

CZE S8 -0.15 (0.13) NOR S30 -0.41 (0.13)

DEU S9 1.50 (0.13) NZL S31 -0.56 (0.13)

DNK S10 -0.29 (0.13) POL S32 0.14 (0.13)

ESP S11 0.68 (0.13) PRT S33 -0.33 (0.13)

FIN S12 0.18 (0.13) ROM S34 -0.73 (0.13)

FRA S13 1.16 (0.13) RUS S35 0.66 (0.13)

GBR S14 0.77 (0.13) SAU S36 -1.20 (0.13)

GRC S15 -0.84 (0.13) SVK S37 -1.08 (0.13)

HUN S16 -0.24 (0.13) SVN S38 -1.02 (0.13)

IDN S17 0.16 (0.13) SWE S39 0.41 (0.13)

IND S18 0.85 (0.13) THA S40 0.22 (0.13)

IRL S19 -1.09 (0.13) TUR S41 0.14 (0.13)

ISL S20 -2.38 (0.13) USA S42 1.76 (0.13)

ISR S21 -0.51 (0.13) VNM S43 -0.34 (0.13)

ITA S22 1.28 (0.13)

47

Table 8 : Bilateral TiVA Equation for OECD Countries

Variable est. s.e.

Distance [0,375) -�d1 -2.23 (0.71)

Distance [375,750) -�d2 -2.87 (0.71)

Distance [750,1500) -�d3 -3.27 (0.67)

Distance [1500,3000) -�d4 -3.86 (0.66)

Distance [3000,6000) -�d5 -4.50 (0.55)

Distance [6000,maximum) -�d6 -4.85 (0.11)

Shared border -�b 0.33 (0.18)

Shared language -�l 0.79 (0.15)

RTA -�f -0.32 (0.35)

Country est. s.e.

Australia S1 -0.34 (0.11)

Austria S2 -0.34 (0.11)

Canada S3 -0.09 (0.11)

Denmark S4 -0.63 (0.11)

Finland S5 -0.38 (0.11)

France S6 0.66 (0.11)

Germany S7 0.97 (0.11)

Greece S8 -1.15 (0.11)

Italy S9 0.73 (0.11)

Japan S10 1.26 (0.11)

Netherlands S11 0.12 (0.11)

New Zealand S12 -1.10 (0.11)

Norway S13 -0.61 (0.11)

Portugal S14 -0.80 (0.11)

Spain S15 0.31 (0.11)

Sweden S16 -0.15 (0.11)

United Kingdom S17 0.28 (0.11)

United States S18 1.27 (0.11)

48

Table 9 : Estimation of Competitiveness Using TiVA

Country est. s.e. Country est. s.e.

AUS S1 0.30 (0.12) ITA S25 1.26 (0.12)

AUT S2 0.18 (0.12) JPN S26 1.76 (0.12)

BGR S3 -1.20 (0.12) KOR S27 1.22 (0.12)

BRA S4 0.89 (0.12) LTU S28 -1.51 (0.12)

CAN S5 0.39 (0.12) LVA S29 -2.16 (0.12)

CHE S6 0.37 (0.12) MEX S30 -0.09 (0.12)

CHL S7 0.07 (0.12) MLT S31 -1.75 (0.12)

CHN S8 1.84 (0.12) MYS S32 0.16 (0.12)

CZE S9 0.06 (0.12) NLD S33 0.57 (0.12)

DEU S10 1.46 (0.12) NOR S34 -0.23 (0.12)

DNK S11 -0.12 (0.12) NZL S35 -0.53 (0.12)

ESP S12 0.79 (0.12) PHL S36 -1.03 (0.12)

EST S13 -1.73 (0.12) POL S37 0.31 (0.12)

FIN S14 0.15 (0.12) PRT S38 -0.35 (0.12)

FRA S15 1.16 (0.12) ROM S39 -0.68 (0.12)

GBR S16 0.78 (0.12) RUS S40 0.93 (0.12)

GRC S17 -0.66 (0.12) SAU S41 -1.71 (0.12)

HKG S18 1.15 (0.12) SGP S42 0.70 (0.12)

HUN S19 -0.12 (0.12) SVK S43 -0.83 (0.12)

IDN S20 -0.32 (0.12) SVN S44 -0.85 (0.12)

IND S21 0.59 (0.12) SWE S45 0.38 (0.12)

IRL S22 -0.71 (0.12) THA S46 0.12 (0.12)

ISL S23 -2.24 (0.12) USA S47 1.79 (0.12)

ISR S24 -0.54 (0.12) VNM S48 0.32 (0.12)

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